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Abstract

The equations of QCD are widely believed to describe the properties of
mesons, baryons and their hadronisation after hard interactions at particle
accelerators such as the LHC. However, the theoretical framework
linking the fundamental Lagrangian of QCD to the mesons and baryons
observed in experiment is still in development. The states observed by
experiments can be investigated using a variety of other theoretical methods.

We consider here two methods, Chiral Perturbation Theory and
carefully considering the poles in a scattering amplitude. In chapters 2
and 3 we apply these methods to determine the composition of the sigma(600) and f0(980) scalar resonances observed in scattering.

In chapter 4 we turn to make the connection between the fundamental
Lagrangian and the observed physics. The first step here is to solve the
Schwinger-Dyson equations for the gluons, ghosts and quarks which describe
how a Green’s function behaves non-perturbatively. We primarily
investigate the coupled gluon and ghost system without quarks. We find
that non–trivial vertices are required to obtain self–consistent solutions
in the simplest truncation and that a solution with a finite ghost dressing
function appears to be preferred.